\(\mathbf {Example\;2.3}\) : Let's analyse first these type of spacetime
variables in the case of standard QFT on a fixed curved spacetime
(\(M,g_{ab})\)  [1]}, [2]}. Consider the usual scalar field
\(\varphi \)  with a linear wave equation
\(g_{ab}\nabla ^{a}\nabla ^{b}\varphi =0.\) 
